We propose a digitally linearized radio-over fiber (RoF) downlink transmitter architecture for cloud radio access networks (C-RANs), and we demonstrate its proof of principle in the near-millimeter wave (mm-wave) range (24 GHz). Amplification of input radio frequency signal power is commonly adopted to minimize the impact of photodetection noise on the dynamic range at the receiver. Unfortunately, this amplification causes the RoF system to behave nonlinearly, leading to distortions during the electrical-optical-electrical conversion process that degrades the overall signal quality. To overcome this problem and linearize the RoF link, we propose and implement effective digital predistortion (DPD) using a memory polynomial model. Experimentally, comparing the error vector magnitude (EVM) of a 64-quadratic-amplitude modulation (QAM) 20-MHz bandwidth (BW) long-term evolution (LTE) signal modulated onto a 24-GHz carrier with and without linearization, we found a signal quality improvement by 4.2%, resulting in an EVM value of 2%. Broader LTE signals of BWs up to 100 MHz were experimentally tested to achieve EVM values below 3.5% after DPD, both for 64 and 256 QAM. It is worth highlighting that the remote radio head (RRH) unit does not require any frequency up conversion to generate the mm-wave signals and the centralized baseband unit can serve multiple remote RRHs operating at different frequencies as in C-RANs. Our results demonstrate the suitability of the proposed C-RAN transmitter architecture for next generation 5G wireless communication networks.